You are correct, ASA and ISO values are identical. However, and almost without exception, all reviews, user's manuals, articles and written material use the term ISO rather than ASA. As such, it is probably worth abandoning the old designation.
The information that you have provided is not enough to give you a definitive answer to your original post, however, almost all of the newer DX cameras will default to the highest ISO that you set in the Auto-ISO menu when you are using the built in flash in low light conditions. It is not a defect, but rather, it is by design. I also find it objectionable and originally thought that it was a firmware flaw. So, if you want a lower ISO value with the flash, you have to turn AUTO-ISO off or limit the top value.
I never use "AUTO" so I can't comment on behavior in that mode. EDITED TO ADD. However, I can tell you that AUTO mode lets the camera select all settings including when it thinks that you should use the built-in flash. Since you obviously use the AUTO-ISO menu settings, as do I, you might be better off to use P (Program) to keep the flash from firing when it is really not needed since you are using high ISO values. Most photos with the built-in flash are somewhat "harsh" in low light.